Alternating flow hydraulic pump circuit

ABSTRACT

A hydraulic pump assembly including a first pump, a second pump, a shaft, and fluid lines is disclosed. The first pump includes a first piston assembly. The second pump including a second piston assembly. Each piston assembly of the first and second pumps includes a cylinder and a piston slidably disposed in the cylinder. The shaft connects the first pump to the second pump and is configured to displace the pistons within the cylinders of the first and second piston assemblies. The fluid lines fluidly couple the first piston assembly with the second piston assembly to form paired piston assemblies. The first piston assembly is phase shifted from the second piston assembly.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Non-Provisional Patent Application claims the benefit of the filing dates of U.S. Provisional Patent Application Ser. No. 62/415,827, filed Nov. 1, 2016, entitled “Alternating Flow Hydraulic Pump Circuit,” the entire teachings of each of which are incorporated herein by reference.

GOVERNMENT SUPPORT CLAUSE

This invention was made with government support under NSF-0540834 awarded by the National Science Foundation. The government has certain rights in the invention.

BACKGROUND

The present disclosure relates to hydraulic pumps circuits. More particularly, it relates to alternating flow hydraulic pumps useful, for example, in multi-actuator hydraulic circuits.

Hydraulics is used for the generation, control, and transmission of power by the use of pressurized liquids. Alternating flow hydraulics (AFH), can be characterized by the transmission of power with no netflow. AFH is the hydraulic analog of alternating current electrical systems, transmits power through waves in liquids, solids and gases. AF fluid power can be classified as an alternating flow or standing wave. In alternating flow, a periodically varying flow source, with no net fluid flow, is used to transmit power. In a standing wave system, the forcing frequency and pipe wavelength are tuned such that reflections at the end of a pipe form standing pressure waves.

Hydraulic machinery uses hydraulic circuits in which hydraulic fluid is pushed, under pressure, through hydraulic pumps, pipes, tubes, hydraulic motors, hydraulic cylinder, etc. to generate power, for example, to move heavy loads. Multi-actuator hydraulic circuits can be included in various hydraulic machinery, from legged robots to excavators. Multi-actuator hydraulic circuits conventionally use metering valves, or proportioning valves, for independent control of each actuator. The majority of existing hydraulic circuits use metering valves to control the fluid flow and pressure to an output line. Metering valves can provide fast and precise control, however, using metering valves can be highly inefficient due to the reliance of dissipating power across a partially open valve. Metering valves throttle the fluid flow to dissipate power as a means of controlling delivered power. Controlling the fluid flow by reducing, or throttling, the fluid flow with metering valves can result in energy loss from the energy that was used to generate the flow and pressure of the fluid to the metering valve. The throttling energy loss associated with valve control is largely the reason that the average efficiency of mobile hydraulic systems is 21%.

A variable displacement pump can be an efficient alternative to using metering valves, in order to control flow to each actuator (i.e., displacement control). Types of variable positive displacement pumps include axial piston pumps, bent axis pumps, vane pumps, linkage pumps, and radial piston pumps. Other types, of variable displacement pumps are also available. In many applications, the variable displacement pumps operate at low displacement for a large portion of the cycle, resulting in significant energy loss. The efficiency of conventional variable displacement pumps can be poor at low volumetric displacements because the largest energy losses are not of equal scale to the output power. Additionally, the variable displacement pumps typically have three times the mass and volume of a fixed displacement gear pump of the same displacement. The most efficient architecture, the bent axis, does not have a through shaft, preventing stacked mounting on a common shaft that can be driven by a prime mover. The next most efficient architecture, the axial piston, has an aspect ratio (i.e., proportional relationship between width and height) that is long axially, resulting in a long packaging space for multiple common-shaft mounted pumps. The radial piston pump can operate at very high pressures and has a very efficient architecture of a mechanical connection from a shaft out to driving pistons within the radial piston pump with very low friction. The radial piston pump can be generally pancake shaped such that the radial piston pump is radially large but axial short. In this manner, multiple pumps can be stacked and directly coupled to an engine to create a multi-actuator circuit. For multi-actuator circuits, it is desirable that multiple pumps package well together to be driven on a common shaft to be driven by a common prime mover. The package size and weight of the pumps can also be important.

Utilizing a variable displacement pump to control each actuator can be an efficient alternative for multiple actuator systems. For example, an excavator employing displacement control with variable displacement pump/motors can have a 39% energy savings over throttling valve control in a load sensing circuit. The modularity of displacement control makes it more reliable than a single pump circuit having throttling valves in that if one component of the system fails, the other components can remain fully functional. Efficiency in displacement control in a hydraulic system can depend on the performance and efficiency of the variable displacement pump across a wide range of displacements and pressures.

An alternative to a mechanically variable displacement pump is to vary the flowrate of a fixed displacement pump through high-speed switching of digital valves, termed digital displacement. The most common approach to digital displacement is flow diverting, where the actively controlled tank valve is held open for a portion of the upstroke of the piston, returning the fluid to a tank. At a specified displacement fraction of the piston stroke, the tank valve is rapidly closed and the pressure valve is opened, sending flow to the load. While this approach eliminates the leakage and friction of port plates of an axial piston or bent axis pump, it has several drawbacks. First, the valve transitions occur at high piston velocity, resulting in throttling energy loss across the partially open tank and pressure valves for a non-negligible fraction of the piston stroke and generating a water hammer event that creates noise and large flow pulsations. Second, viscous flow losses are incurred by pumping the unused flow back to tank. Finally, there is a general lack of digital valves with reasonable energy consumption that can switch fast enough for high-speed pumps.

Variable displacement pumps can be useful to eliminating metering valve control through displacement control. Variable displacement pump architectures can be heavy, are axially long (thus making common-shaft mounting challenging), and have poor efficiency at low displacements. An efficient variable displacement pump with a form factor amenable to a common shaft is desirable. An AF variable pump assembly that is highly efficient, axially short (thus allowing multiple pumps to be mounted on a common shaft), and power dense is desirable.

In light of the above, a need exists for an improved hydraulic pump circuit capable of providing highly efficient control and performance in a compact form and useful, for example, in variable displacement pumps.

SUMMARY

Some aspects of the present disclosure are directed toward a hydraulic pump assembly including a first pump, a second pump, a shaft, and fluid lines. The first pump includes a first set of piston assemblies. The second pump includes a second set of piston assemblies. Each piston assembly of the first and second pumps includes a cylinder and a piston slidably disposed in the cylinder. The shaft connects the first pump to the second pump and is configured to displace the pistons within the cylinders of the first and second sets of piston assemblies. The fluid lines fluidly couple the first piston assembly with the second piston assembly to form paired piston assemblies. The first set of piston assemblies is phase shifted from the second set of piston assemblies.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 diagrammatically illustrates an example alternating-flow hydraulic pump assembly including two pumps in accordance with aspects of the present disclosure.

FIG. 2 diagrammatically illustrates an example pumping chamber of an alternating-flow hydraulic pump assembly in accordance with aspects of the present disclosure.

FIGS. 3A-3E diagrammatically illustrate pistons of an example alternating-flow hydraulic pump in phase at various stages in accordance with aspects of the present disclosure.

FIGS. 4A-4F diagrammatically illustrate pistons of an example alternating-flow hydraulic pump at various stages of a phase shift in accordance with aspects of the present disclosure.

FIGS. 5A-5F diagrammatically illustrate pistons of an example alternating-flow hydraulic pump at various stages of another phase shift in accordance with aspects of the present disclosure.

FIGS. 6A-6E diagrammatically illustrate pistons of an example alternating-flow hydraulic pump at stages of another phase shift in accordance with aspects of the present disclosure.

FIG. 7 illustrates a plot of fractional displacement of an alternating-flow hydraulic pump as a function of phase shifts in accordance with aspects of the present disclosure.

FIG. 8 is plot of the fraction of maximum flow rate versus crankshaft angle at various phase angles according to an example of the present disclosure.

FIG. 9 diagrammatically illustrates a multiple actuator displacement controlled system including AF hydraulic pump assemblies according to aspects of the present disclosure.

FIGS. 10-15 are graphical representations of data acquisition from tests of an example variable displacement pump assembly for displacement control using of alternating flow hydraulics in accordance with aspects of the present disclosure.

DETAILED DESCRIPTION

This disclosure includes an alternating flow (AF) hydraulic pump that varies the flowrate by phase shifting pairs of oscillating pistons. The AF pump assembly in accordance with this disclosure, in one example, can include connecting pairs of pistons of two radial piston pumps and phase shifting the case of one pump with respect to the other pump to vary the displacement. Other types and quantities of pumps are also acceptable in accordance with this disclosure.

One embodiment of an alternating-flow (AF) hydraulic pump assembly 10 in accordance with principles of the present disclosure is diagrammatically illustrated in FIG. 1. The AF hydraulic pump assembly 10 includes the mating of two pumps 20 a, 20 b. The pumps 20 a, 20 b are illustrated in FIG. 1 and described as radial piston pumps; however, other types of pumps can also be used. The pump 20 a includes a set of piston assemblies 21 a, 22 a, 23 a each including a piston slidably disposed in a cylinder. Each piston assembly 21 a, 22 a, 23 a employs a piston 31 a, 32 a, 33 a in such a manner that the piston 31 a, 32 a, 33 a can slide along a longitudinal axis of a respective cylinder 41 a, 42 a, 43 a, for example. Similarly the pump 20 b includes a set of piston assemblies 21 b, 22 b, 23 b each including a piston 31 b, 32 b, 33 b slidably disposed in a cylinder 41 b, 42 b, 43 b. In the embodiment of radial piston pumps, each pump 20 a, 20 b includes a casing 24 a, 24 b housing radially the arranged piston assemblies 21 a, 22 a, 23 a; 21 b, 22 b, 23 b, respectively. In one embodiment, three piston assemblies 21, 22, 23 are arranged radially at 120°. In another embodiment, a single piston assembly is included in each pump 20 a, 20 b (see, e.g., FIG. 2). Other quantities of piston assemblies are also acceptable. Regardless, piston assemblies of the pumps 20 a, 20 b are fluidly coupled in pairs, or mated, with one piston assembly of the pump 20 a coupled to one piston assembly of the pump 20 b. For example, pairs of piston assemblies 21 a and 21 b, 22 a and 22 b, 23 a and 23 b, respectively, of the pumps 20 a, 20 b are fluidly connected.

Each piston assembly is fluidly open to a respective inlet and outlet flow line through openings, or ports, in the casing 24. An inlet flow 30 is split into inlet flow lines 34, 35, 36, with associated valves to control flow into each of the piston assemblies 21 a, 22 a, 23 a, respectively of the pump 20 a. The valves can be passive (e.g., check valves) or active valves that allow the pumps to operate as a motor. A fluid source (not shown) can be fluidly connected to the inlet flow 30. Flow out of each respective piston assembly 21 a, 22 a, 23 a proceeds to the respective paired piston assembly 21 b, 22 b, 23 b of the pump 20 b and then continues to an outlet flow 40 through one of flow lines 44, 45, 46. Flow from each flow line 44, 45, 46 can be controlled with a respective check valve into outlet flow 40. The two pumps 20 a, 20 b share a common crankshaft 26 for rotating a cam 28 of each pump 20 a, 20 b and a manifold (not shown) for combining the flow from piston assembly pairs 21 a, 21 b; 22 a, 22 b; 23 a, 23 b, respectively. The crankshaft 26 extends between each pump 20 a, 20 b to rotate the cams 28, or rotating block, around an axis of rotation in each pump 20 a, 20 b, respectively. The cams 28 are rotated around the axis of rotation with the plurality of piston radially reciprocally moving within corresponding cylinders and moving through a constant length stroke at each cylinder. In one embodiment, the cams 28 are eccentric, although other cam profiles are also acceptable. For example, the cams 28 can include multiple lobes with the lobes of the cam 28 contacting and activating a piston to slidably move in the cylinder as the shaft 26 rotates the cam 28 about an axis of rotation. The cam 128 can provide flexibility with a tunable displacement profile to adjust the displacement density and balance axle forces. Further, the pistons can be driven through a variety of other mechanical constraints, such as a crankshaft and connecting rod, swashplate, or other translating mechanism, for example.

With continued reference to FIG. 1, a phase shift to create an alternating flow with the paired, or linked, pistons can be created by rotating the case of one pump with respect to the other pump. The phase shifting can occur between the pistons of pump 20 b relative to the pistons of pump 20 a to vary the total output flow rate of the pump assembly 10. A combination of phase shifts in a pump assembly including multi-piston pumps can produce variation in fluid displacement. Phase shifting can be implemented by rotationally shifting the case 24 of one of the pumps 20 b relative to the other pump 20 a using hydraulic actuation, for example, with the common shaft 26 extending to and between the pumps 20 a, 20 b. Alternatively, the casings 24 of the pumps 20 a, 20 b are fixed together and a phasor is created in one of the cams 28 to implement and control a rotation relative to the shaft 26. In one example, a phase shift of ϕ can be implemented. Flow can be transferred, or displaced, between the piston assemblies that are paired, or fluidly coupled. Some example phase shifts to vary the displacement are discussed further below.

FIG. 2 is a schematic illustration of an example pumping chamber 50 of an AF hydraulic pump assembly 51 in accordance with aspects of the present disclosure. The pumping assembly 51 includes a first piston 52 a and a second piston 52 b slidably disposed in first and second cylinders 54 a, 54 b, respectively. First piston 52 a can be included with a first, or leading, pump and the second piston 52 b can be included with a second, or lagging, pump, for example. The first and second, or leading and lagging, pumps can operate in cooperation to satisfy a load demand on the system. The first and second cylinders 54 a, 54 b include a first interior portion 62 a, 62 b and a second interior portion 64 a, 64 b fluidly separated by pistons 52 a, 52 b, respectively. A volume of the first interior portions 62 a, 62 b and second interior portions 64 a, 64 b are correspondingly varying with movement of first and second pistons 52 a, 52 b within cylinders 54 a, 54 b. The first and second cylinders 54 a, 54 b are fluidly coupled, or paired, through a pipe 58. Valves 60 a, 60 b, such as spring loaded valves can be included to control fluid flow to the cylinders 54 a, 54 b. The first and second pistons 52 a, 52 b can be attached to a common crankshaft (see e.g., FIG. 1) forming two crank-slider mechanisms 56 a, 56 b for movement of the first and second pistons 52 a, 52 b within the first and second cylinders 54 a, 54 b. The pumping chamber 50 includes the pipe 58 extending between the first and second chambers 54 a, 54 b and the interior portion 62 a, 62 b of the first and second chambers 54 a, 54 b An instantaneous volume of the pumping chamber 50 as a function of the crank angle, θ, and phase shift, ϕ, is described as:

V _(inst)=2V _(TDC) +V _(pipe) +V _(lead) +V _(lag)

V _(lead) =A _(pis) [r(1-cosθ)+L−√{square root over (L ²-r ²sin²θ)}]

V _(lag) =A _(pis) [r(1-cos(θ+ϕ))+L−√{square root over (L ²-r²sin²(θ+ϕ))}]

where V_(inst) is the actual total volume of the pressure chamber, V_(lead) is the actual swept volume of the leading piston, V_(lag) is the actual swept volume of the lagging piston, A_(pis) is the cross-sectional area of the pumping piston, r is the crankshaft eccentricity, L is the connecting rod length, and ϕ is the phase angle. The leading and lagging pistons are rigidly connected and rotatable at the same angular velocity, ω. An effective displacement is defined assuming the piston has ideal sinusoidal motion, which can be realized if L approaches infinity in the above equations. The difference in the waveforms is shown to be negligible for the connecting rod to crankshaft rations. With ideal sinusoidal motion the fractional displacement, X, (see, e.g., FIG. 7) is defined as:

$X = {\cos \frac{\varphi}{2}}$

The total effective displacement per revolution of the pump can then be calculated as:

D=nsA_(pis)X

where n is the number of fluid chambers (each with two pistons) and s is the piston stroke.

FIGS. 3A-3E diagrammatically illustrate paired pistons in phase at various stages in accordance with aspects of the present disclosure. A fluid source T supplies fluid through inlet valve IV and line to the paired piston assemblies and then flow to a load through outlet valve OV and line. Similar to the pumps discussed above, piston A of pump A is fluidly connected to piston B of pump B. In this embodiment, piston A and piston B are in phase (i.e., phase shift, ϕ=0) and slidably move at the same time and frequency. FIG. 3A illustrates both pistons extended downward in the cylinders, for example, at the beginning of a revolution. FIG. 3B illustrates both pistons moving upward (direction of movement indicated with arrows) in unison until the pistons are fully extended within the cylinders as further illustrated in FIG. 3C. In FIG. 3D, both pistons are moving downward in unison until they are returned to the fully extended downward position illustrated in FIG. 3E. In the embodiment illustrated in FIGS. 3A-3E, the combined flow of piston A and piston B of pump A and pump B, respectively, produce twice the flow rate per revolution of the displacement of a single piston. The flow in and out of the pumps in this embodiment is controlled by check valves IV and OV, so as the pistons are moving downward, flow is drawn in from the source S on the left side. When the pistons are moving upward, the left side check valve closes and flow is pushed out of the right OV check valve at the load pressure.

FIGS. 4A-4F diagrammatically illustrate paired pistons at various stages of a phase shift in accordance with aspects of the present disclosure. In this embodiment, piston A and piston B are in phase shift ø=π/3. At this phase shift, piston A and piston B combine to create some output flow and are also creating some shuttling of flow back and forth between piston A and piston B with the offset movement of the pistons with respect to one another (direction of movement indicated with arrows) causing displacement. FIGS. 5A-5F diagrammatically illustrate pistons at various stages of another phase shift in accordance with aspects of the present disclosure. In this embodiment, piston A and piston B are in phase shift ø=2π/3. At this phase shift, additional flow is shuttled between piston A and piston B, reducing the total flow rate out of the pump per revolution of the displacement of piston. FIGS. 6A-6E diagrammatically illustrate pistons at stages of another phase shift in accordance with aspects of the present disclosure. In this embodiment, piston A and piston B are in phase shift ø=π, or 180° out of phase. At this phase shift, there is no flow output from the pump assembly. The entire flow is displaced, or shuttled, back and forth between piston A and piston B.

FIG. 7 is a plot of fractional displacements of an example AF hydraulic pump assembly as a function of a phase shift of sinusoidal pistons. The AF hydraulic pump assembly can include two sinusoidally oscillating pistons of equal displacement with the fluid between the two cylinders directly connected, such as the AF hydraulic pump assembly 50 of FIG. 2. When the motion of the two pistons is in phase, the flow is combined. When the motion of the pistons is 180 degrees out of phase, the pistons shuttle flow back and forth, resulting in zero output flow. Through variation of the phase shift of the two pistons, the combined displacement is continuously variable, as shown with plot line 70 of FIG. 7.

FIG. 8 is plot of a crankshaft angle (in radians) versus a fraction of maximum flow rate at various phase angles according to an example of the present disclosure. Phase angles (ϕ)) of 0, π/4, π/2, 3π/4, and π are graphically illustrated in FIG. 8. In this example, the flow rates of a three cylinder pump or a pair of three cylinder pumps of a pump assembly are illustrated. Flow can be transferred between the piston assemblies that are paired, or fluidly coupled. The fluidly coupled pistons can be disposed physically near one another and, thus, can have short fluid paths and for mechanical efficiency. The flow rate out of a three cylinder pump (or pump assembly) can include six flow pulses per full revolution of the pump as illustrated for each of the phases included. Pressure ripples corresponding to the flow pulses can be created. The use of multiple cam lobes increases the number of pumping strokes per revolution of the pump and hence the pump displacement.

FIG. 9 diagrammatically illustrates a multiple actuator displacement controlled system 200 including AF hydraulic pump assemblies according to aspects of the present disclosure. Multiple pumps Pump 1, Pump 2, . . . . Pump N can be stacked and directly coupled to an engine to create a multi-actuator circuit. A prime mover 210 is coupled to Pump 1, Pump 2, . . . . Pump N. Actuators 211, 212, 213... (e.g., hydraulic actuators) can be used to drive various degrees of freedom of a machine. For example, in an excavator, actuator 211 that is driven by Pump 1 can control the boom, actuator 212 driven by Pump 2 can control the stick, and actuator 213 driven by Pump N can control the bucket. In one example, the multiple actuator displacement controlled system 200 is a radial piston architecture. A radial piston architecture can be useful as the AF pump for efficiency, a short axial package allowing multiple pumps to be easily common-shaft mounted for a multi-actuator displacement control system, and high displacement density achievable in a radial pump using a multi-lobe cam to create multiple pumping strokes per revolution.

In one example, multiple actuator displacement controlled system 200 includes a four-quadrant hydraulic pump assembly. Four-quadrant hydraulic pump assemblies can be highly efficient across the full range of displacements and is axially short (compact) is employed. In one example, disc style check valves are employed, for fast valve closing. Other types of valves that allow full four-quadrant pump/motor operation are also acceptable. Active valves can enable four-quadrant control, which allows energy regeneration for increased system efficiency. With four-quadrant operation, the input shaft can be loaded during pumping and absorbing regenerative energy during motoring. The regenerative energy can be transferred through the common shaft to pumps driving other degrees-of-freedom, reducing the load on the prime mover and hence further improving the system efficiency. The four-quadrant pump is an excellent fit in displacement control applications where the combination of high efficiency and energy regeneration capabilities will improve the overall hydraulic system efficiency. The modularity of the displacement control circuit can improve system reliability as a single component failure will not influence the other degrees-of-freedom. The four-quadrant hydraulic pump can enable efficient, high-bandwidth displacement control for multi-actuator displacement control systems.

EXAMPLE

FIG. 10-15 are graphs representing data acquisition from tests of an example variable displacement pump assembly for displacement control using of alternating flow hydraulics (AFH) in accordance with aspects of the present disclosure. The variable displacement in this example is generated by the relative phase angle between piston pairs connected by a rigid pipe. When the pistons are in phase, the pump displacement is at a maximum that is twice that rated for the individual pumps, in this case two Cat Pumps® 3CP1120's. The crankshafts of the two fixed displacement pumps were connected via a sprocket-and-chain transmission which allowed accurate measurement of the phase. The AF pump's efficiency was measured for 8 different phase angles with an efficiency of near 90% at full displacement and 65% at 36% displacement.

In one example, the measured system pressure, flowrate, input torque, and shaft speed was used to measure the total efficiency of the pump, given as:

$\eta_{total} = {\frac{P_{sys}Q_{sys}}{T\; \omega} = {\eta_{m}\eta_{v}}}$

where P_(sys) is the output system pressure of the pump, Q_(sys) is the output flowrate from the pump, T is the average input torque, and ω is the average shaft speed. The total efficiency can also be considered as the product of the pump's mechanical efficiency, η_(m), and volumetric efficiency, η_(v). The mechanical efficiency characterizes the mechanical losses within the system such as piston-cylinder friction, bearing friction, any internal fluid friction, and in this case, friction from the sprocket-chain transmission. The mechanical efficiency is defined as:

$\eta_{m} = \frac{P_{sys}D}{2\pi \; T}$

where D is the total effective displacement per revolution which is given by D=nsA_(pis)X, as discussed above. The volumetric efficiency describes the amount of leakage and compressibility losses within the system, defined as:

$\eta_{v} = \frac{2\pi \; Q_{sys}}{D\; \omega}$

The different phase angles were realized by disassembling the chain-and-sprocket transmission and rotating one of the sprockets on its associated crankshaft. The speed of the pump was managed by a hydraulic motor which was controlled by a flow control valve. To measure the crankshaft angle of each pump, a block with dowel pins was slid into a pair of the machined holes in the sprocket mounted to the crankshaft. The machined holes align with the keyway of the crankshaft at top dead center (TDC) of cylinder 1. A digital angle gauge was used to measure the angle of the leading crankshaft and the lagging crankshaft and the difference between the two was the phase shift. Pressure, flowrate, torque, and optical encoder sensors were all read with a PCIe-6353 National Instruments DAQ board on a desktop computer. A series of experiments were run at all discrete phase angles achievable with the chain and sprocket. Once the transmission was installed and the phase angle was measured, the pump was driven by a hydraulic motor controlled with a flow control valve. For each experiment, the speed of the pump and load were set simultaneously due to the load being an adjustable orifice. Once the speed and pressure were set, the data acquisition (DAQ) of acquired data was for 3 seconds at a rate of 10 kS/s.

The example pump operated smoothly across the full range of displacements, speeds, and pressures investigated. Pressure versus volume curves are also illustrated in FIGS. 10 and 11, at 2 degrees and 165 degrees phase shift, respectively. The volume (in cubic meters) represents the volume of fluid or the current volume within the fluid chamber and the pressure is the pressure of the fluid inside the pressure chamber. The pressure versus volume curves also include simulation data from the numerical model of the AF pump. The measured and simulated torque at the input crankshaft are shown in FIG. 12 for a phase angle of 2 degree. The average flowrate is plotted versus the measured flow rate in FIG. 12.

The pressure measured in the fluid chambers on either side of the connecting pipe are plotted versus time in FIG. 13. The maximum phase allowed for this prototype was 165 degrees. Plots of the mechanical, volumetric, and total efficiency are shown in FIG. 13. While the experiment was run at 250, 500, 750, and 1000 RPM the efficiencies between the datasets varied by only approximately 3%, therefore the average value for each displacement is plotted in FIG. 14.

Two different pressure versus volume curves are illustrated in FIGS. 10 and 11, both showing a full cycle of the AF pump at 500 RPM and 75 bar. The 2 degree case shows a typical trace for a pump at full displacement, with near vertical compression and decompression cycles and overshoot of the set pressure in the top-right corner of the curve. This overshoot indicates the performance of the check valve. As the pressure across the valve exceeds the cracking pressure, it rapidly opens, the dynamics of which can be modelled as a spring-mass-damper. The model agrees well with the pressure versus volume plots except for the 165 degree case once the pressure in the chamber starts to decrease, as shown in the top-left portion of FIG. 11. Some insight into what may be happening at this point in the cycle can be seen in FIG. 14 where about halfway through the compressed volume cycle there is a dip in pressure of 10 bar. The numerical model was not able to capture this effect well, which is evident in the pressure versus volume curves, but does not affect the measured and modelled efficiency curves. This is likely due to the piston motion not being perfectly sinusoidal due to the kinematics of the crank-slider a slight negative change in the total volume of the two cylinders at the high phase shift angle.

The numerical model correlates well with the experimental results except for the higher phase angles where there is a small discrepancy. This is magnified in the volumetric efficiency plot, shown in FIG. 15. As the displaced volume compared with the cylinder volume is quite small at the high phase shift angles, inaccuracies in the predicted fluid stiffness as well as the non-sinusoidal piston displacements become magnified. The plot does illustrate good agreement between the predicted and measured mechanical efficiency.

The volumetric, mechanical, and total efficiencies for the example and model are illustrated in FIG. 15. The efficiencies are plotted with respect to fractional displacement and not phase angle. The efficiency of this variable displacement pump is comparable with some existing pump architectures, with a peak efficiency near 90% at full flow and 65% at 36% displacement. The high efficiencies can be attributed to the shuttling of fluid between the two pistons in the single pressure chamber for the realization of partial displacements.

Although the present disclosure has been described with reference to preferred embodiments, workers skilled in the art will recognize that changes can be made in form and detail without departing from the spirit and scope of the present disclosure. 

What is claimed is:
 1. A hydraulic pump assembly, comprising: a first pump including a first piston assembly, wherein the first piston assembly includes a first cylinder and a first piston is slidably disposed in the first cylinder; a second pump including a second piston assembly, wherein the second piston assembly includes a second cylinder and a second piston is slidably disposed in the second cylinder; a shaft connecting the first pump to the second pump and configured to displace the first and second pistons within the first and second cylinders; and fluid lines to fluidly couple the first piston assembly with the second piston assembly to form paired piston assemblies, wherein the first piston assembly is phase shifted from the second piston assembly.
 2. The assembly of claim 1, wherein the first and second pumps each include at least two piston assemblies.
 3. The assembly of claim 1, wherein the first and second pumps are radial piston pumps.
 4. The assembly of claim 1, wherein the first and second piston assemblies each include three piston assemblies arranged radially at 120 degrees.
 5. The assembly of claim 1, wherein the first and second pumps are inline pumps.
 6. The assembly of claim 1, wherein the fluid lines include: an inflow source line for fluid flow into the first and second piston assemblies; and an outflow source line for fluid flow out of the first and second piston assemblies.
 7. The assembly of claim 6, further comprising: active valves disposed along the inflow source line to control flow into the first and second piston assemblies.
 8. The assembly of claim 2, wherein each of the at least two piston assemblies of the first pump is fluidly coupled to one of the at least two piston assemblies of the second pump.
 9. The assembly of claim 1, further comprising: at least one additional first and second pumps including pump assemblies, wherein the shaft connects the at least one additional first and second pumps and wherein the fluid lines extend between the at least one additional first and second pumps to fluidly couple piston assemblies to form pairs of mated piston assemblies, and wherein the piston assemblies are phase shifted from one another.
 10. A hydraulic pump assembly, comprising: a first pump and a second pump each including: a piston assembly, a translating mechanism to selectively move a piston within a cylinder of the piston assembly, and a casing to house the translating mechanism and piston assembly; a shaft coupled to the first and second pumps, the shaft to jointly rotate the translating mechanisms; and a fluid line to fluidly couple the piston assemblies of the first and second pumps; wherein the pistons are movable by the translating mechanisms to transfer fluid flow between the fluidly coupled piston assemblies.
 11. The assembly of claim 10, wherein the piston assembly of each of the first and second pumps includes at least two piston assemblies.
 12. The assembly of claim 11, wherein each of the at least two piston assemblies of the first pump is fluidly coupled to one of the at least two piston assemblies of the second pump.
 13. The assembly of claim 10, wherein first pump is phase shifted from the second pump along the shaft.
 14. The assembly of claim 10, wherein the casings of the first and second pumps are rotationally fixed along the shaft.
 15. The assembly of claim 10, wherein the first and second pumps each have an axis of rotation, wherein the translating mechanisms are rotatable around the axes of rotation to move the pistons of the piston assemblies.
 16. A method of operating a hydraulic pump assembly, comprising: supplying fluid to a first pump and a second pump mounted along a shaft, the first and second pumps each including a piston assembly, a translating mechanism to selectively move a piston within a cylinder of the piston assembly, and a casing to house the translating mechanism and piston assembly; rotating the translating mechanism s of the first and second pump; slidably moving the piston of the first pump within the cylinder in response to contacting the piston of the first pump with the translating mechanism; transferring fluid from the piston assembly of the first pump to the piston assembly of the second pump; slidably moving the piston of the second pump within the cylinder in response to contacting the piston of the first pump with the translating mechanism; and transferring fluid from the piston assembly of the second pump to the piston assembly of the first pump.
 17. The method of claim 16, wherein the first pump is rotated relative to the second pump.
 18. The method of claim 16, wherein the translating mechanisms are rotated relative to the shaft and the first and second pumps are rotationally fixed to the shaft.
 19. The method of claim 16, wherein slidably moving the pistons of the first and second pumps includes radially reciprocally moving the pistons within the cylinders through a constant length stroke.
 20. The method of claim 16, wherein the first and second pumps are oriented at a phase shift angle. 